CAJ | 학술논문

针对一类具有空间不均匀性的辨识和回归问题，提出了基于小波分析的极限学习机方法。从多分辨率分析的思想出发，构造一簇紧支撑正交小波作为隐层激活函数，并利用改进的误差最小化极限学习机训练输出层权重，避免了新加入高分辨率子网络后的重新训练。同时，由一维多分辨分析的张量积构造了二维多分辨小波极限学习机。进而通过脊波变换将小波学习机扩展到高维空间，对脊波函数的伸缩、方向和位置参数进行优化计算。对具有奇异性的函数仿真结果证明，与标准极限学习机相比，小波极限学习机由于其聚微性能在极短的训练时间内更好地逼近目标。一些实际基准回归问题上的测试验证了脊波极限学习机在其中大部分问题上达到更高的训练和泛化精度。
침대일류구유공간불균균성적변식화회귀문제，제출료기우소파분석적겁한학습궤방법。종다분변솔분석적사상출발，구조일족긴지탱정교소파작위은층격활함수，병이용개진적오차최소화겁한학습궤훈련수출층권중，피면료신가입고분변솔자망락후적중신훈련。동시，유일유다분변분석적장량적구조료이유다분변소파겁한학습궤。진이통과척파변환장소파학습궤확전도고유공간，대척파함수적신축、방향화위치삼수진행우화계산。대구유기이성적함수방진결과증명，여표준겁한학습궤상비，소파겁한학습궤유우기취미성능재겁단적훈련시간내경호지핍근목표。일사실제기준회귀문제상적측시험증료척파겁한학습궤재기중대부분문제상체도경고적훈련화범화정도。
An extrme learning machine ( ELM) algorithm based on wavelet transform was designed for a class of indentification and regression problem with inhomogeneity in a space. From the standpoint of multiresolution analysis, a set of compactly supported or-thogonal wavelets was constructed as the hidden layer activation function, and the output layer weight of the network was trained by an error minimized extreme learning machine. This method avoided retraining the output layer parameter as adding a subnetwork with high-er resolution. The wavelet ELM was then extended into a two-dimensional space using the tensor product of a scaling function. To hur-dle high-dimensionality issues, ridgelet transform based on ELM was obtained, whose scaling, direction, and position parameters were determined by optimization methods. Simulation results on functions with singularity confirm that the wavelet ELM can approch the tar-get better. When being tested on some real benchmark problems, the ridgelet ELM demonstrates better training and testing accuracy on most cases.